What is the minimum percentage of the popular vote required to win the electoral vote in the USA?

Small states have a decided advantage in the number of electoral votes per capita they cast in US presidential elections. If the electoral vote winner won every tiny, winner-take-all state by just one vote, and big states went for 100% for the loser of the electoral vote, how skewed could the election results get? I heard a commentator on a TV show claim that it would be theoretically possible to win the electoral vote with just 22% of the popular vote. Is our current Electoral College system really that crazy? If it is, how great a margin do you think would be needed before the public demanded pure representative elections?